Gurvirender Tejay
02/04/2004
INFO 790: Theory of Information
Empirics
The logic of secrecy was the mirror image of the logic of information. (Colin Burke 1994)
Empirics represent one of the branches of Semiotics (the study of signs). Empirics is the
study of the physical characteristics of the medium of communication. It is concerned
with the signals used to code and transmit the message. Empirics involves the study of
communication channels and their characteristics like sound and electronic transmission.
It is generally associated with Shannon’s (1948) A Mathematical Theory of
Communication also referred to as information or communication theory. In this paper I
briefly introduce two separate works of Shannon (1949) and Hill (1929) from the field of
cryptology that can be considered at the level of empirics. Cryptology is the science of
(overt) secret writing (cryptography), of its unauthorized decryption (cryptanalysis), and
of the rules which are in turn intended to make that unauthorized decryption more
difficult (encryption security) [Bauer:2000]. It has become popular in protecting
communication channels, databases, and software. In terms of modern mathematics,
cryptology shows traits of statistics, combinatory algebra, and stochastics. Shannon’s
(1949) work “Communication Theory of Secrecy Systems” involves stochastics, whereas
Hill’s (1929) “Cryptography in an Algebraic Alphabet” involves combinatory algebra.
Shannon’s work in cryptography was presented in terms of communication theory.
Shannon considered secrecy system as almost identical with a noisy communication
system. His work was based on the idea of redundancy in language. A message with less
redundancy had a cryptogram that was more difficult to crack. Shannon demonstrated
how to make cryptograms more difficult to decipher as well as how much encrypted text
is needed to decipher it to the original message. Shannon’s paper “Communication
Theory of Secrecy Systems” is an application of communication theory in the field of
cryptology. It has a theoretical approach and is concerned with general mathematical
structure and properties of secrecy systems. The paper introduces a model of secrecy
systems and defines it abstractly as a set of transformation of one space (the set of
possible message) into a second set (the set of possible cryptograms). Among its
limitations, the paper only addresses the “true” secrecy systems and is concerned with the
case of discrete information where the message to be enciphered consists of a sequence of
discrete symbols, each chosen from a finite set. The paper is divided into three parts. The
first part addresses the basic mathematical structure of secrecy systems. The second part
is concerned with the problem of “theoretical secrecy” while the final part deals with
“practical secrecy.”
Hill’s paper “Cryptography in an Algebraic Alphabet” involved combinatory algebra and
was concerned with general linear substitutions. In particular, Hill proposed selfreciprocal homogenous linear substitutions (with N=26). He designed a mechanical
device with geared wheels for linear substitutions (n=6). Here n represents the encryption
width. These machines were used for superencrypting three-letter code groups of radio
call signs. Hill’s cipher system had a great impact upon cryptology. Since his invention
the value of mathematical methods in cryptology has been unchallenged.
Gurvirender Tejay
02/04/2004
Reference
1. Bauer, F.L. (2000), Decrypted Secrets: Methods and Maxims of Cryptology. New
York: Springer.
2. Hill, L.S. (1929). “Cryptography in an Algebraic Alphabet.” The American
Mathematical Monthly, 36:306-312.
3. Shannon, C.E. (1949). “Communication Theory of Secrecy Systems.” Bell
System Technical Journal, 28:656-715.